Experiment2. Average m:i/gal Accepted Value = :NIPG =

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1 Experiment2 Measurement and the Metric System 2-1 Objectives 1. To become acquainted with physical measurement techniques (both direct and indirect methods). 2. To learn how to read and record data to the proper number of significant figures. 3. To become familiar with the metric system. 4. To practice unit conversions involving met1i.c units. Discussion Measurements are basic to any scientific pursuit. A measurement has both a magnitude (numerical value) and a unit. Metric and S.I. units are used in the sciences. In our daily lives, approximations of temperature, distance, etc. are often sufficient. In the laboratory, however, measurements must be more accurate to be of any value. Due to inexact tools and faulty observations, measurements are subject to error; they are never absolutely exact..most measurements are made from a scale. Data should generally be recorded to one decimal place beyond what is calibrated on the scale. This requires estimating ' 1 between the linesrr to determine the last digit. For more detail and practice with measurements see, the section titled Measurement in your chemistry 4 supplement. Measurements are typically performed several times during any particular experiment. Each time a measurement or set of measurements is made, the measurement (or set of measurements) is called a trial. Three is typical (and the minimum) number of trials performed in an experiment. Since each measurement has some uncertainty, the average results from the trials is considered the experimental result. To illustrate, the average mileage for a Ford 1998 F-150 pickup truck was determined by ''experimentation." Three sets of data were collected during.january Trial Date Miles Traveled Gallons Used Gas Mileage # (mi) (gal) (mil~g-al, or :MPG) '.J.. 1/13/ / /17/ Average m:i/gal The result of this experiment - the experimental value - is l\/ipg. A curious scientist and consumer would want to know how dose this value is to the estimate made by the Environmental Protection Agency (EPA). The EPA 1 s estimate for the mileage for this vehicle is MPG. One way to show how close the experimental value is to the EPA estimate is to determine the difference between the two values. The next question is; do you subtract the EPA estimate from the experimental value, or vice versa? The convention is to subtract the accepted value (the EPA estimate) from the experimental value. Thus the difference can be calculated as follows: Experimental Value l\1pg Accepted Value = :NIPG = :MPG The difference, MPG, gives three pieces of information. First it gives the!(direction" that the experimental result is off from the EPA estimate, that is negative, this means that the experimental value is smaller than the accepted value. Second it gives the magnitude of the difference between. the two l\/ipg values, Finally, it gives the units. The difference between the experimental result and the accepted value is a good way to compare an experimental value with an accepted value, however, it is not the best way to express the error in an e~--periment.

2 To illustrate. assume that the 1V1PG for an economv car was determined bv its owner to be l\1pg and the EPA estimate is JMPG. Given these two ;alues we have: Ex-perimental Value lvipg Accepted Value = 32.SOMPG = 0.28 MPG Notice that the magnitude of the difference in each "experiment" is 0.28 IvlPG. Although these two differences are the same, the difference for the F-150 tvipg is more significant than the difference for the economy car. This is because 0.28 is a larger percentage of the accepted value of MPG for the F-150 than that for the economy car. The percent error is a better way to express an error relative to an accepted value. The percent error is a way to express bow close an experimental result is to the accepted value and in what "direction" that result is off relative to the accepted value. The percent error is calculated using the following formula: Percent Error... Experimental Value - Accepted Value x 100 Accepted Value Shown in the table below is a comparison of percent error and a simple difference calculation. Notice that the percent error for the :F-150 is greater than that for the economy car. Automobile Experimental MPG EPA MPG Percent Error F-150 Economy % -i-0.86% The experimental result may be greater than, less than or equal to (rarely) the accepted value. This leads to percent errors that may be positive, negative.or zero. ln this experiment, linear dimensions, masses, volumes and temperatures will be measured. These quantities can be easily measured using common equipment. Often two measurements are combined in order to define a new quantity. For example, the mass divided by the volume of a given sample of matter defines density, a physical property characteristic of a given substance. Some of your results will be compared to accepted values by calculation of percent errors. You will be expected to calculate percent errors for many of the experiments that you perform in this course.

3 Procedure :-3 A. Densitv of a Liquid Weigh a drv 50 ml graduated on the ele<..'tronic balance. "Masses should be recorded to the nearest hundredth of a gram (0.0X g) when using the electronic balance. Add about 15 ml of distilled water, from a squeeze bottle, to the graduate and determine the volume to the nearest tenth of a milliliter (0.X ml). Now measure the mass of the graduate containing the liquid. From the data, calculate the mass of the distilled water in the graduated and compute the density of distilled water. Record the temperature of the water to the nearest tenth of a degree Celsius (0.X C). Use the table on page 2-4 to find an accurate value of the density of distilled water at your experimental temperature. Repeat the same experiment using approximately 30 ml and then 45 ml of distilled water. B. Density of a Solid Obtain a copper metal and an unknown metal from the stockroom. Record the sample number that is stamped on the unknown. metal. Determine the mass of the using the electronic balance (O.OX g). Place about 30 ml of water in a 50 ml graduate and record the volume (O.X ml). Tilt the graduate and gently slide the copper into the water; avoid splashing and spilling. Record the new volume and use the data to calculate to volume of the copper. Calculate the density of the copper, and using the theoretical density of copper calculate the percent error. Determine the density of the unknown metal in the same manner that you used for the copper. After calculating the density of the unknown metal, obtain the theoretical density from the instructor. C. Indirect Determination of the Thickness of One Sheet of Paper and the Mass ofl.00 Square Centimeter of One Sheet of Paper Obtain a packet of paper from the middle of the lab. Be sure to record the color and tare weight of the packet. Using a platform balance, determine the mass (0.0X g) of the packet (250 sheets) of paper provided. Measure the thickness, length, and width of the packet in centimeters (0.0X cm). Do the calculations and unit conversions indicated on the data and calculations table. D. Indirect Determination of the Mass and Volume of One Drop of : Using the electronic balance, determine the mass (0.0X g) of a dry, 10 ml graduated._ Now add 60 drops of distilled water and record the volume (O.OX ml). Weigh the graduate containing the 60 drops of water. Do the calculations and unit conversions indicated on the data and calculation table. E. Introduction to the Metric Svstem l. Obtain from the stockroom or your instructor a ruler that has at least a 1/16 inch scale on one edge and a centimeter scale on the other edge. 2. Measure each of the five lines on page 2-7 with each scale. a. Measure a line in centimeters; being careful to estimate the open space between the scale marks. b. Measure the same line in inches; being careful to estimate the open space. It is often more reliable to record English length data as a sum to be performed on your calculator. A typical reading and conversion to decimal notation is: r , Fractional ' 4" + 3/4 11 r /16" : Decimal 0.75" " : Decimal 4" ' 1 1_ ~ ,. -..: r--~ = Certain "digits" give an unlimited number of significant figures. Uncertain (doubtful) "digitsu give a limited number of significant figures. The doubtful digit here limits the decimal answer to the hundredths place

4 Experiment 2 Name: MEASUREMENTS AND THE METRIC SYSTEM A. Density of a Liquid Empty 50-mL Graduated Cylinder Approximatively 15 ml Approximatively 30 ml Approximatively 45 ml Total Mass of the Cylinder and its Content Mass of Volume of Density of 0.00 g 0.0 ml Average Density of (from the three measurements) Accepted Density = g/ml Percent Error (Show work.) D. Indirect Determination of the Mass and Volume of One Drop of Mass of the Dry Graduated Cylinder Number of Drops of Added Mass of the Volume of Mass of Volume of One Drop of Mass of One Drop of drops ml ml/drop = µl/drop /drop = µg/drop

5 B. Density of a Solid Sample Copper Cylinder Unknown Metal Cylinder Number: Trial 1 Trial 2 Trial 1 Trial 2 Mass of the metal Initial volume: volume of water alone in the graduated Final volume: combined volume of water and the metal submerged Volume of the metal Density of the metal Accepted density 8.96 g/cm g/cm 3 NOT GIVEN Percent error NO CALCULATION IS REQUIRED